
"""simple docstring"""



def 			_UpperCamelCase						(    _A   )     ->	int:





    """simple docstring"""

    _UpperCAmelCase        = [1]

    _UpperCAmelCase     ,_UpperCAmelCase     ,_UpperCAmelCase        = 0, 0, 0
    _UpperCAmelCase        = ugly_nums[ia] * 2
    _UpperCAmelCase        = ugly_nums[ia] * 3
    _UpperCAmelCase        = ugly_nums[ia] * 5

    for _ in range(1       ,   UpperCamelCase_   ):
        _UpperCAmelCase        = min(UpperCamelCase_       ,   UpperCamelCase_       ,   UpperCamelCase_   )
        ugly_nums.append(UpperCamelCase_   )
        if next_num == next_a:
            ia += 1
            _UpperCAmelCase        = ugly_nums[ia] * 2
        if next_num == next_a:
            ia += 1
            _UpperCAmelCase        = ugly_nums[ia] * 3
        if next_num == next_a:
            ia += 1
            _UpperCAmelCase        = ugly_nums[ia] * 5
    return ugly_nums[-1]


if __name__ == "__main__":
 from doctest import testmod

 testmod(verbose=True)
 print(F"{ugly_numbers(2_0_0) = }")
def 			lowercase(	UpperCamelCase_							,					UpperCamelCase_       )		->	List[str]:







 '''simple docstring'''
 _enforce_args(UpperCamelCase_							,					UpperCamelCase_       )
 if n == 0:
  return 0
 UpperCamelCase			  =      float("""-inf"""       )
 for i in range(1							,					n + 1       ):
  UpperCamelCase			  =      max(
      UpperCamelCase_							,					prices[i - 1] + naive_cut_rod_recursive(n - i							,					UpperCamelCase_       )       )

 return max_revue





def 			lowercase(	UpperCamelCase_							,					UpperCamelCase_       )		->	Optional[Any]:







 '''simple docstring'''
 _enforce_args(UpperCamelCase_							,					UpperCamelCase_       )
 UpperCamelCase			  =      [float("""-inf"""       ) for _ in range(n + 1       )]
 return _top_down_cut_rod_recursive(UpperCamelCase_							,					UpperCamelCase_							,					UpperCamelCase_       )





def 			lowercase(	UpperCamelCase_							,					UpperCamelCase_							,					UpperCamelCase_       )		->	List[Any]:







 '''simple docstring'''
 if max_rev[n] >= 0:
  return max_rev[n]
 elif n == 0:
  return 0
 else:
  UpperCamelCase			  =      float("""-inf"""       )
  for i in range(1							,					n + 1       ):
   UpperCamelCase			  =      max(
       UpperCamelCase_							,					prices[i - 1] + _top_down_cut_rod_recursive(n - i							,					UpperCamelCase_							,					UpperCamelCase_       )							,					)

  UpperCamelCase			  =      max_revenue

 return max_rev[n]





def 			lowercase(	UpperCamelCase_							,					UpperCamelCase_       )		->	Union[str, Any]:







 '''simple docstring'''
 _enforce_args(UpperCamelCase_							,					UpperCamelCase_       )

 # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
 # length 0.
 UpperCamelCase			  =      [float("""-inf"""       ) for _ in range(n + 1       )]
 UpperCamelCase			  =      0

 for i in range(1							,					n + 1       ):
  UpperCamelCase			  =      max_rev[i]
  for j in range(1							,					i + 1       ):
   UpperCamelCase			  =      max(UpperCamelCase_							,					prices[j - 1] + max_rev[i - j]       )

  UpperCamelCase			  =      max_revenue_i

 return max_rev[n]





def 			lowercase(	UpperCamelCase_							,					UpperCamelCase_       )		->	Union[str, Any]:







 '''simple docstring'''
 if n < 0:
  UpperCamelCase			  =      f"""n must be greater than or equal to 0. Got n = {n}"""
  raise ValueError(UpperCamelCase_       )

 if n > len(UpperCamelCase_       ):
  UpperCamelCase			  =      (
      """Each integral piece of rod must have a corresponding price. """
      f"""Got n = {n} but length of prices = {len(UpperCamelCase_       )}"""
  )
  raise ValueError(UpperCamelCase_       )





def 			lowercase(	)		->	str:







 '''simple docstring'''
 UpperCamelCase			  =      [6, 10, 12, 15, 20, 23]
 UpperCamelCase			  =      len(UpperCamelCase_       )

 # the best revenue comes from cutting the rod into 6 pieces, each
 # of length 1 resulting in a revenue of 6 * 6 = 36.
 UpperCamelCase			  =      36

 UpperCamelCase			  =      top_down_cut_rod(UpperCamelCase_							,					UpperCamelCase_       )
 UpperCamelCase			  =      bottom_up_cut_rod(UpperCamelCase_							,					UpperCamelCase_       )
 UpperCamelCase			  =      naive_cut_rod_recursive(UpperCamelCase_							,					UpperCamelCase_       )

 assert expected_max_revenue == max_rev_top_down
 assert max_rev_top_down == max_rev_bottom_up
 assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
     main()
